[填空题]
A population of 50 hamsters was int d 1pjp4tkg2o7tg)up6v), hriroduced to a kiob*zc*9,d 6qqw y1,xob 7ii new town. One month later, the number of hamsters was 62 . The number of ha*od6 9bq*, icq7wxziy1,k oibmsters, P , can be modelled by the function
P(t)=50 $\times b^{t}, \quad t \geq 0$
where t is the time, in months, since the hamsters were introduced to the town.
1. Find the value of b .
2. Calculate the number of hamsters in the town after 6 months.
A wildlife specialist estimates that the town has enough water and food to support a maximum population of 2000 hamsters. ≈
3. Calculate the number of months it takes for the hamster population to reach this maximum. ≈
